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$$\scriptsize{\overset{{\large{\textbf{Mark Distribution in Previous GATE}}}}{\begin{array}{|c|c|c|c|c|c|c|c|}\hline \textbf{Year}&\textbf{2019}&\textbf{2018}&\textbf{2017-1}&\textbf{2017-2}&\textbf{2016-1}&\textbf{2016-2}&\textbf{Minimum}&\textbf{Average}&\textbf{Maximum} \\\hline\textbf{1 Mark Count}&2&0&2&2&3&3&0&2&3 \\\hline\textbf{2 Marks Count}&2&4&2&3&2&3&2&2.7&4 \\\hline\textbf{Total Marks}&6&8&6&8&7&9&\bf{6}&\bf{7.3}&\bf{9}\\\hline \end{array}}}$$

# Featured Questions in Algorithms

1
Let $G = (V,E)$ be an undirected connected simple (i.e., no parallel edges or self-loops) graph with the weight function $w: E \rightarrow \mathbb{R}$ on its edge set. Let $w(e_{1}) < w(e_{2}) < · · · < w(e_{m})$ ... we replace each edge weight $w_{i} = w(e_{i})$ by its square $w^{2}_{i}$ , then $T$ must still be a minimum spanning tree of this new instance.
2
The graph shown below has $8$ edges with distinct integer edge weights. The minimum spanning tree (MST) is of weight $36$ and contains the edges: $\{(A, C), (B, C), (B, E), (E, F), (D, F)\}$. The edge weights of only those edges which are in the MST are given in the figure shown below. The minimum possible sum of weights of all $8$ edges of this graph is_______________.
3
The number of distinct minimum spanning trees for the weighted graph below is _____
Let $G_1=(V,E_1)$ and $G_2 =(V,E_2)$ be connected graphs on the same vertex set $V$ with more than two vertices. If $G_1 \cap G_2= (V,E_1\cap E_2)$ is not a connected graph, then the graph $G_1\cup G_2=(V,E_1\cup E_2)$ cannot have a cut vertex must have a cycle must have a cut-edge (bridge) has chromatic number strictly greater than those of $G_1$ and $G_2$
Consider the following algorithm for searching for a given number $x$ in an unsorted array $A[1..n]$ having $n$ distinct values: Choose an $i$ at random from $1..n$ If $A[i] = x$, then Stop else Goto 1; Assuming that $x$ is present in $A$, what is the expected number of comparisons made by the algorithm before it terminates? $n$ $n-1$ $2n$ $\frac{n}{2}$
Consider the following C program that attempts to locate an element $x$ in an array $Y[ \ ]$ using binary search. The program is erroneous. f (int Y[10] , int x) { int u, j, k; i= 0; j = 9; do { k = (i+ j) / 2; if( Y[k] < x) i = k;else j = k; } while (Y[k] != x) && (i < j)) ; if(Y[k] ... $x > 2$ $Y$ is $[2 \ 4 \ 6 \ 8 \ 10 \ 12 \ 14 \ 16 \ 18 \ 20]$ and $2 < x < 20$ and $x$ is even